Wednesday, 8 January 2014

Can financial economics learn from Dancing with the Stars?

Carola Binder (@cconces) brought my attention to a paper by Paul Rubin that was his presidential address to the Southern Economic Association. What caught my attention was the paper is concerned with fear of markets (he coins the term 'emporiophobia' - fear of merchants or markets) that Prof Rubin associates with the emphasis economics places on competition rather than cooperation. These themes resonate with me, since I believe that central to the Fundamental Theorem of Asset Pricing, the key theory of Financial Mathematics, is the concept of reciprocity, and this reflects a profound relationship between mathematics, markets and ethics. In particular, I hold a somewhat perverse view that it is not markets that degrade public morality, but society degrades commercial morality. In my mind, Rubin's paper holds implicit support for my views.

Rubin observes that economics adopts the competition metaphor from sport, citing Deirdre McCloskey who is important for me because she introduced me to contemporary Virtue Ethics. This struck me as significant because I do not encourage my five year old son, who is showing all the sporting feebleness of his father, to participate in sport because I think sport is concerned, primarily, with competition.

An aspect that Virtue Ethics and Pragmatism share is that there are 'goods internal to practices', here 'goods' do not mean 'commodities', but things that are 'good'. MacIntyre explains (p 188) that if a child is encouraged to play chess by offering them sweets if they win, they will see chess as an avenue to sweets and fail to recognise the 'goods internal' to the practice of chess (developing a particular analytic skill). As a result they will see no fault in cheating, in order to receive sweets. The ethical problem is the child is focusing on goods external (sweets) to the practice of chess.

When Prof Rubin states

Sports are specifically competitive; the entire purpose of the activity is to determine the winner.

he is, in my opinion, wrong. For me there are more interesting internal goods in sports. I encourage my son to play sport because it helps him socialise and understand teamwork; it helps his physical development; as he gets older pursuit of excellence in sport develops his ability to achieve objectives, something that is at the heart of Strictly Come Dancing (Dancing with the Stars). Could the economist Paul Rubin explain why hundreds of thousands sports fans spend money supporting teams that are unlikely to win anything, if the essence of sport is about competition and winning. In fact we are disgusted when the 'external good' of winning comes to dominate sport: Lance Armstrong. The financial corollary is, and on this point I believe Prof Rubin and I are in agreement, is that the internal good of markets is in creating ties that bind (enabling exchange), the external good is making money.

What I think Prof Rubin highlights is MacIntyre's 'disquieting suggestion' that modern moral philosophy has become so separated from ethics that it is incapable of making moral judgments. Rubin attempts to defend markets by claiming the error originates in adopting sporting metaphor. I would argue the error is in failing to appreciate the goods internal to practices, which is because there is an emphasis on the consequences of actions, rather than their character. Both Virtue Ethics and Pragmatism identify current problems emerging during the Enlightenment, Pragmatism objects to Cartesian Representaionalism while MacIntyre sees broader issues emerging out of Individualism and Autonomy. These observations challenge what it is to be a contemporary scientist.

While I agree with most of MacIntyre's argument, we would probably not agree on economic issues, and in fact I do diverge with many who advocate applying Virtue Ethics to transform contemporary financial practice and the point of contention is on the significance of scarcity.

The earliest Greek text that addresses economic questions was Works and Days written by the poet Hesiod around 750 BCE, pre-dating the scientist-philosopher Thales buy some one hundred years. The poem starts with the myth of Pandora, relating the strife of mankind to the introduction of technology and goes on to identify the role that scarcity has in determining human behaviour -- the gods make life a struggle for mankind, and so we have to work hard. The archaeological record for the Aegean at this time suggests that climate change led to a long running famine and there was migration from the main city-states into new areas for farming. Hesiod's father had been a farmer and merchant in north-western Anatolia, but the recession had forced him to move to Boeotia in modern Greece. The contemporaneous Biblical story of the Fall is similar, after eating from the tree of knowledge humans are expelled from the Garden of Eden. In the British Isles We see evidence of extensive trade networks with the large quantities of axe-heads that seem to have been used in commerce, compared with the forts that characterise the Iron Age, centres of control over resources.

Following the sack of Rome by the Goths in 410 CE, Augustine of Hippo wrote The City of God against the Pagans. The book

Censures the pagans, who attributed the calamities of the world, and especially the recent sack of Rome by the Goths, to the Christian religion, and its prohibition of the worship of the gods

The pagans were arguing that the destruction of Rome, a disastrous event that impoverished the city, was a consequence of Christianity. Augustine countered, and laid the foundations of the Catholic Church, by offering a Platonic argument that the corporeal world was an unnatural state for the Christians, who would eventually return to The City of God. To counter Pelagian and Donatist heresies Augustine argued against free-will and while he agreed with the Stoics about the uselessness of divination and astrology in predicting the future, he disagreed with the pagan view that God had no foreknowledge

God knows all things before they come to pass, and that we do by our free will whatsoever we know and feel to be done by us only because we will it . ... all wills also are subject [to God], since they have no power except what He has bestowed upon them.

In his book On free choice of the will Augustine employs mathematical analogies to convince his audience that there are transcendental truths

For those inquirers to whom God has given the ability ... [can see that] the order and truth of numbers has nothing to do with the senses of the body, but that it does exist, complete and immutable, and can be seen in common by everyone who uses reason

Augustine is incorporating the immutability and indubitablity of mathematics as Catholic dogma.

Between 1000--1300 CE Europe underwent a period of economic expansion that had saw the population double while the amount of coin in circulation increased six-fold. Driving the expansion was a rise in temperature that led to greater agricultural productivity, population growth and after the late twelfth century, an expansion of commerce, centred on the Mediterranean, and an urban explosion.
Moses ben Maimon (Maimonides) argued in his Guide for the Perplexed, written in 1190 and an influence on Aquinas, that God's punishment after the Fall of Man was not so much about scarcity but uncertainty. In the Garden of Eden humans had perfect knowledge, which was lost with the Fall, and it is the loss of this knowledge which is at the root of suffering - if we know what will happen we can manage scarcity. The thirteenth century saw the ultimate flowering of European thought that laid the foundations for the scientific revolution of the seventeenth century.

The great expansion of Latin Christianity went into reverse at the start of the fourteenth century. Between 1315 and 1322 abnormally cold winters were separated by abnormally wet or dry summers, harvests failed leading to the Great Famine in which about 10% of the population died in some urban areas. These famines were followed in 1347 by the Black Death, and by 1350 the plague had spread throughout Europe, causing the death of, in places, a third of the population, hitting the poor and urban communities particularly hard. The plague was not a single event, but reappeared, and the successive calamities of the 1320s, 1350s and then 1360s would have traumatised society. The influence of the Church suffered as clerics were disproportionately infected by plague, since they cared for the sick, and it proved unable to protect people from the disease. The Scholastics, using either faith or reason, were unable to explain what was happening around them, and in the words of the historian William Bouwsma, they failed to "give to life a measure of reliability and thus reduce, even if it cannot altogether abolish, life's ultimate and terrifying uncertainties''.

After Latin Christianity lost its empire in the Eastern Mediterranean the Crusades were replaced by dynastic conflicts. While England and France had strong monarchies, fighting each other in the Hundred Years War between 1337 and 1453, the Holy Roman Empire and Italy became fragmented. Merchant cities on the Atlantic and Baltic coasts exerted their independence from German princes, who themselves had vast estates and were capable of challenging the Emperor. The cities of northern Italy became dominated by signori while the Papacy and the Kingdom of Naples, which had driven European culture in the twelfth century, became a pawn for the French and Spanish/Hapsburg monarchies.

The agricultural collapse in northern Europe and disruptive wars led to a collapse in commerce, particularly hard hit were the Flemish towns, who had emerged as centres of trade following Philip IV the Fair's suppression of the Champagne Fairs between 1305 and 1309. The primary concern of the autocrats was the maintenance of their power, power which was based on armies manned by mercenaries that needed to be paid: Pecunia nervus belli, `money is the sinew of war'. The subtleties of Scholastic economic analysis would be replaced by demand for scarce gold and silver.

By the start of the sixteenth century the scarcity associated with the previous centuries was replaced by uncertainty. The anxiety of the fourteenth and fifteenth centuries resulted in Calvin's revival of strict Augustinian theology which proved popular among mercantile communities that were growing as wealth and power moved from the Mediterranean to the Atlantic following the discovery of the Americas. Confessional wars erupted, in France, the Netherlands, Central Europe and the British Isles. The Dutch Wars, initially stimulated by high Hapsburg taxation resulted in the rebels paying a higher tax burden but significant developments in public finance enabled the Dutch to successfully fund their rebellion. Key in this process was Simon Stevin, the abaco trained mathematician who established the Dutch Mathematical School that inspired Descartes. The Thirty Years War, characterised by bellum se ipse alet, `let war pay for itself', resulted in widespread devastation, but the 'Gothic atrocity narrative' that emerged during Romanticism, was re-evaluated in the twentieth century, and contemporary historians argue that "Sudden changes in fortune became a defining characteristic of the conflict'' .

In England 1665 saw Plague; 1666 the Great Fire; 1672 The Great Stop of the Exchequer; 1673 an Act of Common Council that looked to put an end to "usurious contracts, false Chevelance, and other crafty deceits'' ; an unsuccessful revolution in 1685, a successful one in 1688; there was a stock-market boom in the early 1690s, with around 40% of the trades between 1692 and 1695 being in stock options; 1694 saw the The Million Adventure Lottery and the creation of the Bank of England; in 1696 was the re-coining, precipitating what has been described as "the gravest economic crisis of the century'' that was partially resolved by Isaac Newton; 1697 saw the first legislation "To Restrain the number and ill Practice of Brokers and stock-jobbers'' being passed. The turbulence of these thirty-two years see the creation of the City of London that is familiar today and laid the foundations of Britain's Empires over the next three hundred years.

The frequentist approach to probability began to dominate the ethical treatment of probability following the claimed defeat, or taming, of chance by mathematics with the publication of Montmort's Analytical Essay on Games of Chance of 1708 and De Moivre's The Measurement of Chance, of 1711 developed in The Doctrine of Chances of 1718. All these texts were developed more in the context of gaming than in the analysis of commercial contracts, which had been the focus of the work of Pascal, Huygens and Bernoulli. The Doctrine was the more influential, introducing the Central Limit Theorem, that independent random variables will be Normally distributed, a result that can be used to argue that asset prices should be log-Normally distributed, as in the Black-Scholes-Merton model. In addition, in 1735 it was being argued that the achievements of the seventeenth century probabilists from Huygens to de Moivre superseded the classical approach to probability, dividing events into the certain, probable and unpredictable, in that it measured probability and changed the status of the `unpredictable'.

It is remarkable that the development of mathematical probability was undertaken almost exclusively by Augustinians: Pascal was a Jansenist; Huygens, Bernoulli and de Moivre were Calvinists; Montmort had been trained to be an Augustinian but renounced orders to marry. This observation is compounded by the facts that Newton was an Arian/Anglican and Leibniz a Lutheran and neither did significant work in probability, Fermat was a Catholic living in the mixed Calvinist/Catholic city of Toulouse. As Augustinians the probabilists all believed in God's pre-destination and omniscience: they denied the existence of randomness, events were unpredictable because man could not understand God's intentions. Over the course of the next hundred years the implicit determinism of the Augustinians became a standard feature of Western science, being codified by Laplace in the 1820s.

From the mid-eighteenth century Romanticism, emphasising an individual genius' emotional reaction to nature, emerged to eclipse the Classical rationalism of the previous century. By the end of the century, Thomas Malthus captured the anxiety of the English rural middle-class following the Terror of the French Revolution in An Essay on the Principle of Population that focused on scarcity.

At the height of Romanticism in 1836 John Stuart Mill defined political economy as being

concerned with [man] solely as a being who desires to possess wealth, and who is capable of judging the comparative efficacy of means for obtaining that end.

and defended Malthus in Principles of Political Economy of 1848, written at a time when Europe was struck by the Cholera pandemic of 1829-1851 and the famines of 1845-1851. Alfred Marshall, synthesised Mill's approach to economics with Darwinian metaphors of competition to lay the foundations of neo-classical economics. Marshall's 1890 definition of economics would be paired down by Lionel Robbins in 1932 as "the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses''.

In the years before the First World War economic policy, particularly interest rates that governed credit, was dominated by the gold-standard, while after the Second World War it was Bretton-Woods. The collapse of Bretton-Woods in August 1972 had an immediate impact on interest-rates. In the 27 years between 1945 and autumn 1972, the Bank of England changed its lending rate 43 times, in the 27 years after 1972, it changed them 223 times. A key economic factor had gone from being fairly stable to being a random process. Similarly, as the US dollar fell in value, price setting mechanisms in commodities, notably oil, collapsed. It was in this environment that financial derivatives made a re-appearance after having been dormant for half a century.

The first academic paper by the mathematician Kolmogorov had been in economic history, when he submitted it he was told that "You have supplied one proof of your thesis, and in the mathematics that you study this would perhaps suffice, but we historians prefer to have at least ten proofs.''. The purpose of the preceding narrative is not to prove a historical fact but to demonstrate that there is an ebb an flow between society being concerned with scarcity or with uncertainty, a distinction made explicitly by ben Maimion.

I suggest that when faced with scarcity, society responds by focusing on individuality and acquisition while when society is challenged by uncertainty it turns to communality, seeking to diversify risks. Aristotlean Virtue Ethics have flourished during periods of growth and exapansion and have declined during periods of scarcity. this explains the rise of utility maximisation as dealing with scarcity in a Romantic context of the individual genius struggling against nature, can be explained, but I propose that since the 1960s society has been focussed more on uncertainty than scarcity and is struggling to shift the economic paradigm in response to the change environment.

This opens up a debate as to whether we face uncertainty or scarcity at the moment, but I see the obsession with scarcity, and the associated fear of change, as a degenerate state. People enjoy Strictly/Dancing with the Stars because it tells a tale of heroic and optimistic pursuit of excellence, and I think this is our natural state.

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About Me

I am a Lecturer in Financial Mathematics at Heriot-Watt University in Edinburgh. Heriot-Watt was the first UK university to offer degrees in Actuarial Science and Financial Mathematics and is a leading UK research centre in the fields.

Between 2006-2011 I was the UK Research Council's Academic Fellow in Financial Mathematics and was involved in informing policy makers of mathematical aspects of the Credit Crisis.